Mean-Quadratic Variation (MQV) portfolio optimisation as an alternative to Time-consistent Mean-Variance (TCMV) optimisation

Peter Van Staden

This talk investigates the Mean-Quadratic Variation (MQV) portfolio optimisation problem and its relationship to the Time-consistent Mean-Variance (TCMV) portfolio optimisation problem. We discuss conditions under which the two problems are (i) identical with respect to Mean-Variance trade-offs, and (ii) equivalent, i.e. have the same value function and optimal control. In order to compare the MQV and TCMV problems in a more realistic setting which involves investment constraints and modelling assumptions for which analytical solutions are not known to exist, we present an efficient partial integro-differential equation (PIDE) method for determining the optimal control for the MQV problem and discuss the associated convergence proof. We show that MQV investor achieves essentially the same results concerning terminal wealth as TCMV investor, but the MQV-optimal investment process has more desirable risk characteristics from the perspective of long-term investors with fixed investment time horizons. As a result, MQV portfolio optimisation is a potentially desirable alternative to TCMV optimisation.

Bio: Pieter van Staden is a PhD student at UQ studying Mathematical and Computational Finance with Dr Duy-Minh Dang as supervisor. Pieter’s PhD is concerned with the numerical solution of portfolio optimisation problems arising from mean-risk objectives (risk being measured by for example variance, quadratic variation, or conditional Value-at-Risk), under realistic modelling assumptions and investment constraints.

Prior to his PhD studies, Pieter completed a BEng (Industrial Engineering) and a BSc (Hons) Financial Engineering at the University of Pretoria (South Africa), as well as a MSc (Mathematics of Finance) at the University of Oxford. In addition, he has held financial risk management positions in both retail and investment banking. For the last 4 years prior to the commencement of PhD studies, Pieter managed the team of actuarial and quantitative analysts responsible for the methodology and maintenance of all Credit Risk and Credit Pricing models used within Nedbank Corporate and Investment Bank (Nedbank CIB) in South Africa.